Spectral triples and Gibbs measures for expanding maps on Cantor sets

DOI10.4171/JNCG/106zbMath1260.37017arXiv1009.5887MaRDI QIDQ692855

Richard Sharp

Publication date: 6 December 2012

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5887

zbMATH Keywords

Cantor setGibbs measureDixmier tracetransfer operatorspectral tripleexpanding map

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Noncommutative measure and integration (46L51) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Noncommutative geometry (à la Connes) (58B34) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (5)

Spectral triples for subshifts ⋮ Spectral metric spaces for Gibbs measures ⋮ Spectral triple and Sinai-Ruelle-Bowen measures ⋮ A classification of aperiodic order via spectral metrics and Jarník sets ⋮ Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples

Cites Work

• Fredholm modules on P.C.F. self-similar fractals and their conformal geometry
• Singular traces and compact operators
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Spectral triples and Gibbs measures for expanding maps on Cantor sets